Presuppositions of Standard Model?

The lambda-CDM model predicts a nearly flat spatial curvature at scales larger than the the scale of homogeneity of the universe. The calculation of many of its parameters depend on the cosmic distance ladder which in turn depend on many observational techniques and statistical comparisons.

My questions are:

1. Have all of these myriad calculations been done in a manner which does not presuppose a nearly flat spatial universe?

2. Many of the observations leading to both the lambda-CDM model and the cosmic distance ladder are taken at distances far below the scale of homogeneity where no assumption of nearly flat curvature can be made (voids and filaments, for example). How has this been taken into consideration?

All of the predictions of these models are impressive but have they been shown to be independent of presuppositions of flatness?

ΛCDM models don't assume flatness. They have various parameters that are fit to the data, like the average density of baryonic matter, etc. One of the outputs is the average spatial curvature. This curvature just happens to be within error bars of zero based on current observations. They also don't assume perfect homogeneity. When you see graphs of the intensities of multipole moments, with fits to the model, that model is clearly not assuming homogeneity, because otherwise the intensities of all the multipole moments (beyond l=0) would be zero.

Certainly. But there is no assumption that the curvature is zero, and there is no assumption that the average densities are such as to cause zero curvature.

Well, to be a bit pedantic, it isn't always assumed that the spatial curvature is zero. Often it is assumed to be zero, simply because the particular observation in question isn't sensitive to the curvature.

You only get a strong constraint on the curvature if you combine very far-away observations (e.g. CMB observations) with nearby observations (e.g. the distribution of galaxies, supernovae). And when we combine near data with far data, spatial curvature is constrained to be zero to within about 1% of the total energy density of the universe.